st: Heckman vs Tobit

Hi All,
I appreciate your feedback on the following questions.
I would like to compare the results of Heckman and Tobit. As I understand, the
estimates from both models (Heckman and Tobit) are not directly comparable and
I have to compute the marginal effects on the probability of selection (y>0)
The steps are as follows:
1. Run Heckman:
. heckman pforeign Z1 Z2 Z3, twostep select (dforeign = X1 X2 X3 X4 Z1 Z2 Z3)
dforeign (selection) is a dummy variable whether foreign are present or not and
pforeign (regression) is the % of foreign.
After heckman, I run mfx:
. mfx compute, eqlist(dforeign) (predict, psel)
If I would like to compute the marginal effect of the independent variables on
the probability of being observed. Is this appropriate?
2. I run a Tobit. The ultimate goal is to compare the results of both
approaches.
. tobit pforeign X1 X2 X3 X4 Z1 Z2 Z3, ll ul
I run mfx:
mfx compute, predict(pr(0,.))
However, there are two other variants of mfx (tobit case):
mfx compute, predict(e(0,.))
mfx compute, predict(ystar(0,.))
Which one computes the marginal effects of the independent variables on the
probability of being observed (positive foreign or pforeign>0)? Is the computed
Tobit marginal effects directly comparable to those from Heckman?
A final question, if I would like to compare Heckman to Tobit, does this mean I
have to compare first step estimates (marginal effects) of Heckman (Probit) to
the Tobit or both equations of Heckman (Probit and OLS) to the Tobit?
Thank you in advance for your clarifications.
Omrane
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